Question: Simplify $\sqrt{7\cdot 2}\cdot \sqrt{2^3\cdot 7^3}$.
Solution: We have:

$\sqrt{7\cdot 2}\cdot \sqrt{2^3\cdot 7^3}=\sqrt{2^4\cdot 7^4}=\sqrt{14^4}=14^2=\boxed{196}$.